A medication is administered intravenously, and the concentration of the drug in a patient’s bloodstream t hours after injection is modeled by
C(t)=t+25t(0≤t≤8).
Concentration C(t) is measured in milligrams per liter (mg/L).
(a) Determine C′(t) and evaluate C′(1). Show all steps.
(b) Using the value of C′(1), write the equation of the line tangent to the graph of C at t=1.
(c) Interpret the meaning of the slope found in part (a) in the context of the medication. Include appropriate units.
(d) Use the tangent line from part (b) to approximate the drug concentration at t=1.2 hours. Comment on whether this approximation is likely to overestimate or underestimate the actual concentration, citing evidence from the function’s behavior.